Calculation Method for Stress, Strain and Displacement Fields of Submarine Tunnels under Hydro-Mechanical Coupling Conditions

Abstract

The present invention belongs to the technical field of tunnel engineering, and provides a calculation method for the stress-strain and displacement fields of strain-softening surrounding rock of a submarine tunnel under the condition of water-hydraulic coupling. It fully considers the interaction between the strain softening of the surrounding rock and the seepage effect, and believes that the hydro-mechanical parameters reflecting the seepage effect, such as the Biot coefficient, the permeability coefficient, etc., change with the change of the confining pressure and plastic strain after excavation. The calculation method for the stress-strain and displacement fields of strain-softening surrounding rock of a submarine tunnel under the condition of water-hydraulic coupling provides a good reference significance and theoretical basis for the stability evaluation of the surrounding rock of a submarine tunnel.

Description

Technical Field

[0001] The present invention belongs to the technical field of tunnel engineering, and particularly relates to a calculation method for stress, strain and displacement fields of submarine tunnels under the condition of water-hydraulic coupling. Background Technique

[0002] In recent years, the construction of submarine tunnel projects in China has reached a climax. As one of the most advanced transportation methods for crossing complex geological conditions such as rivers, lakes and seas, submarine tunnels have developed rapidly due to their advantages of safety, high efficiency, environmental friendliness and little influence by external conditions. However, collapses and sudden water inrushes may occur in the surrounding rock of submarine tunnels, posing great challenges to the safe construction of tunnels.

[0003] During tunnel construction, due to the action of stress release after tunnel excavation, the stress field of the surrounding rock near the tunnel excavation surface is redistributed, resulting in obvious strain softening, reducing the strength of the tunnel surrounding rock, and further reducing the stability of the submarine tunnel surrounding rock. At the same time, for submarine tunnels with deep water levels, the overlying surrounding rock has continuous water supply, resulting in high pore water pressure in the surrounding rock. The increase in the pore water pressure of the tunnel surrounding rock will reduce the effective stress and mechanical strength of the surrounding rock, further reducing the stability of the surrounding rock. Using theoretical methods to calculate the stress, strain field and displacement field of the surrounding rock is one of the important means to analyze the stability of submarine tunnels.

[0004] For the current theory, there are few studies considering both the strain softening and seepage effect of tunnel surrounding rock. In these few studies, hydraulic parameters reflecting the seepage effect such as Biot coefficient and permeability coefficient are usually regarded as fixed values. However, in fact, these parameters change with the change of confining pressure and plastic strain after excavation. This shows the limitations of the current calculation method. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides a calculation method for stress, strain and displacement fields of submarine tunnels under the condition of water-hydraulic coupling to solve the problems in the prior art. The technical solution adopted by the present invention is as follows:

[0006] A calculation method for stress, strain and displacement fields of submarine tunnels under the condition of water-hydraulic coupling includes the following steps:

[0007] Step 1, represent the permeability of the surrounding rock mass of the submarine tunnel by the seepage volume force, and use the seepage volume force and the mechanical equilibrium differential equation of the i-th ring of rock mass as the control equation of seepage action;

[0008] Step 2, adopt the linear Mohr-Coulomb yield criterion as the control equation of the plastic state;

[0009] Step 3: Take the plastic shear strain as the softening parameter, and use the relationships among the plastic shear strain, the radial strain, tangential strain, and radial displacement of the rock mass in the i-th ring, the relationship between the elastic strain and plastic strain, and the relationship between the radial plastic strain and tangential plastic strain as the control equations for the strain-softening phenomenon of the rock mass.

[0010] Step 4: Provide the elastic strain of the rock mass in the i-th ring through the generalized Hooke's law. and the relationships with the Biot effective stresses σ′ r,(i) and σ′ θ,(i) to obtain the seepage differential equation of the rock mass in the i-th ring.

[0011] where and are the radial elastic strain and tangential elastic strain of the tunnel surrounding rock respectively, and σ′ r,(i) and σ′ θ,(i) are the radial effective stress and tangential effective stress respectively.

[0012] Step 5: Ensure the continuity of the radial effective stress, pore water pressure, and displacement of the submarine tunnel surrounding rock at the adjacent ring boundaries by setting boundary conditions.

[0013] Step 6: Obtain the pore water pressure of each ring of rock mass according to the seepage differential equation in Step 4 and the boundary conditions in Step 5.

[0014] Step 7: The water inflow of each ring of rock mass is a constant value, i.e.:

[0015] Q1 = … = Q n = Q

[0016] Calculate the water inflow of the rock mass and update the expression of the pore water pressure simultaneously.

[0017] Step 8: Represent the degree of damage of the rock mass fissures with plastic strain, perform non-linear surface fitting on the sorted test data of the permeability coefficient, and obtain the non-linear surface fitting formulas of the permeability coefficient, Biot coefficient, Poisson's ratio, and elastic modulus affected by the confining pressure and plastic shear strain.

[0018] Step 9: Obtain the stress and displacement in the seepage-invariant elastic region according to the second and fourth boundary conditions in Step 5.

[0019] Step 10: Solve the stress-strain and displacement fields in the elastic zone.

[0020] Step 11: Solve the stress-strain and displacement fields in the plastic zone.

[0021] Step 12: Obtain the plastic shear strain of the submarine tunnel surrounding rock.

[0022] Step 13: Derive the calculation formula for the plastic shear strain within the plastic zone of the surrounding rock of the undersea tunnel.

[0023] The present invention has the following beneficial effects: Starting from the two parts of the governing equation and boundary conditions of hydro-mechanical coupling, this invention introduces the calculation formulas for the pore water pressure and water inflow of the surrounding rock of the undersea tunnel in the seepage equation, and fits the iterative calculation formula that conforms to the variation characteristics of the hydro-mechanical parameters of the surrounding rock based on the experimental data of predecessors. It fully considers the interaction between the strain softening of the surrounding rock and the seepage effect, and believes that the hydro-mechanical parameters reflecting the seepage effect, such as the Biot coefficient and permeability coefficient, change with the change of the confining pressure and plastic strain after excavation. Then, based on the governing equation, boundary conditions, seepage equation, and parameter fitting equation, the calculation formulas for the radial effective stress, tangential effective stress, radial displacement within the elastic-plastic zone of the surrounding rock of the undersea tunnel under seepage action, and the plastic shear strain of the rock mass within the plastic zone are derived, laying a theoretical foundation for the verification and analysis of the hydro-mechanical coupling analytical solution of the undersea tunnel. Description of the Drawings

[0024] Figure 1 Variation law of the permeability coefficient affected by the confining pressure and plastic shear strain;

[0025] Figure 2 Variation law of the Biot coefficient affected by the confining pressure and plastic shear strain;

[0026] Figure 3 Variation law of the Poisson's ratio affected by the confining pressure and plastic shear strain;

[0027] Figure 4 Variation law of the elastic modulus affected by the confining pressure and plastic shear strain;

[0028] Figure 5 Flowchart of the example of the hydro-mechanical coupling analytical solution. Detailed Implementation Manner

[0029] Next, in combination with the Figures 1-5 in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. If not specifically specified, the technical means used in the embodiments are the conventional means well known to those skilled in the art.

[0030] To solve the technical problems existing in the technical background, the present invention provides a calculation method for the stress-strain and displacement fields of strain-softening surrounding rock of a submarine tunnel under the condition of water-hydraulic coupling, which fully considers the interaction between the strain softening of the surrounding rock and the seepage effect, and believes that the hydro-mechanical parameters reflecting the seepage effect, such as the Biot coefficient, permeability coefficient, etc., change with the change of the confining pressure and plastic strain after excavation. The calculation method for the stress-strain and displacement fields of strain-softening surrounding rock of a submarine tunnel under the condition of water-hydraulic coupling provides a good reference and theoretical basis for the stability evaluation of the surrounding rock of a submarine tunnel.

[0031] Step 1, during the excavation of the submarine tunnel, the seepage effect is extremely important for the analysis of the stability of the surrounding rock of the submarine tunnel. During the seepage process, the seepage volume force represents the permeability of the rock mass of the surrounding rock of the submarine tunnel, and the seepage volume force and the mechanical equilibrium differential equation of the i-th ring of rock mass are used as the control equation of the seepage effect.

[0032] The specific expression of the seepage volume force is:

[0033]

[0034] The specific expression of the mechanical equilibrium differential equation of the i-th ring of rock mass is:

[0035]

[0036] Where:

[0037] σ′ r,(i) and σ′ θ,(i) are the radial effective stress and the tangential effective stress respectively;

[0038] r is the calculated radius of the i-th ring of rock mass;

[0039] S i is the seepage volume force;

[0040] The subscript i is the variable value corresponding to the i-th ring of rock mass when r = R i ;

[0041] Step 2, the plastic state of the rock mass of the submarine tunnel is also determined by the yield criterion. The present invention considers the currently most widely used linear Mohr-Coulomb yield criterion as the control equation of the plastic state.

[0042] The specific expression of the linear Mohr-Coulomb yield criterion is:

[0043]

[0044] In the formula, H is a function of the radial effective stress and plastic shear strain of the surrounding rock, and H can be expressed as:

[0045]

[0046] Wherein, c i and are the cohesion and internal friction angle of the rock mass, respectively.

[0047] Step 3: For the strain softening phenomenon of the rock mass, the softening parameter controls the change of the hydro-mechanical parameters of the rock mass. In the present invention, the plastic shear strain is used as the softening parameter. The relationships between the plastic shear strain, the radial strain, tangential strain and radial displacement of the rock mass in the i-th ring, the relationship between the elastic strain and plastic strain, and the relationship between the radial plastic strain and tangential plastic strain are used as the control equations for the strain softening phenomenon of the rock mass.

[0048] The specific expressions for the relationships between the radial strain, tangential strain and radial displacement of the rock mass in the i-th ring are as follows:

[0049]

[0050] Wherein:

[0051] ε r,(i) and ε θ,(i) are the radial strain and tangential strain of the tunnel surrounding rock;

[0052] u (i) is the radial displacement of the surrounding rock.

[0053] The specific expressions for the relationship between the elastic strain and plastic strain are as follows:

[0054]

[0055] Wherein:

[0056] and are the radial elastic strain and tangential elastic strain of the tunnel surrounding rock, respectively.

[0057] The specific expressions for the relationship between the radial plastic strain and tangential plastic strain are as follows:

[0058]

[0059] Wherein, ψ i is the dilation angle of the rock mass in the i-th ring.

[0060] Step 4: During the deformation and seepage processes of the submarine tunnel surrounding rock, the hydraulic characteristics affect the mechanical response, which is the water-mechanical coupling effect. For a fully water-mechanical coupling problem, both the elastic strain and plastic strain are caused by the changes in pore water pressure and stress. Therefore, the generalized Hooke's law provides the relationship between the elastic strain and of the rock mass in the i-th ring and the Biot effective stresses σ′ r,(i) and σ′ θ,(i) :

[0061]

[0062] In the formula:

[0063] G i is the shear modulus;

[0064] μ i is the Poisson's ratio;

[0065] p′0 is the effective hydrostatic ground stress.

[0066] For the axisymmetric plane problem, the seepage effect only occurs radially. Then, the seepage differential equation of the rock mass in the i-th ring is obtained, and its expression is:

[0067]

[0068] In the formula:

[0069] is the pore water pressure of the rock mass in the i-th ring.

[0070] Step 5, in order to ensure the continuity of the radial effective stress, pore water pressure, displacement, etc. of the surrounding rock of the submarine tunnel at the adjacent ring boundary during the process of the hydro-mechanical coupling analytical solution. The boundary conditions for the hydro-mechanical coupling analysis of the present invention are:

[0071]

[0072] In the formula:

[0073] is for r≥R u the initial pore water pressure;

[0074] is the pore water pressure at r = R1;

[0075] σ′ r,1 is the radial effective stress at r = R1;

[0076] σ′ r(n) is the radial effective stress when the radius approaches infinity.

[0077] Step 6, the submarine tunnel is constantly affected by seawater. The seepage effect of seawater will weaken the strength of the surrounding rock mass of the tunnel, and the tunnel excavation will also cause mechanical changes in the surrounding rock, resulting in seepage of the seawater in the pores of the surrounding rock. According to the seepage differential equation in step 4) and the boundary conditions in step 5), the pore water pressure of each ring is obtained, and its expression is:

[0078]

[0079] In the formula:

[0080] γ w is the unit weight of water;

[0081] Q i is the water inflow of the i-th ring of rock mass;

[0082] k i is the permeability coefficient of the i-th ring of rock mass.

[0083] Step 7, during the seepage process, since the flow of seawater obeys the continuity equation, the water inflow of each ring of rock mass is a constant value, that is, Q1 = … = Q n = Q; where Q is the water inflow of the rock mass used in the calculation; adding the left and right sides of the pore water pressure expressions of n rings, the calculation formula for the water inflow of the rock mass can be obtained.

[0084]

[0085] In the formula,

[0086] According to the formula for water inflow, the expression of pore water pressure can be updated as:

[0087]

[0088] Step 8, according to the elastoplastic theory, the degree of damage of rock mass fractures can be represented by plastic strain. Similar to the evolution of hydro-mechanical parameters of strain-softening rock masses, during the formation and cracking of rock mass fractures, fluid parameters such as Biot coefficient and permeability coefficient change with the change of confining pressure and plastic strain. However, in the previous research on analytical solutions, most of them ignored the characteristics of the change of Biot coefficient and permeability coefficient with the change of confining pressure and plastic strain. The present invention organizes the experimental results and data on the change law of permeability coefficient by predecessors and finds that the permeability coefficient is affected by confining pressure and plastic shear strain. Nonlinear surface fitting is performed on the sorted experimental data of permeability coefficient, such as Figures 1-4 . The nonlinear surface fitting formulas for the permeability coefficient, Biot coefficient, Poisson's ratio and elastic modulus affected by confining pressure and plastic shear strain can be obtained, and the specific expressions are as follows.

[0089] From Figure 1 the specific expressions of the permeability coefficient in the elastic region and plastic region are fitted respectively, as follows:

[0090] k = 2.5×10 -7 σ -4.12 -1.2×10 -15 σ + k0

[0091]

[0092] FromFigure 2 The specific expressions of the Biot coefficient in the elastic region and the plastic region are fitted as follows:

[0093] β = 7.6×10 -5 σ -0.56 - 1.2×10 -8 σ + β0

[0094]

[0095] From Figure 3 The specific expressions of the Poisson's ratio in the elastic region and the plastic region are fitted as follows:

[0096] μ = 4.6×10 -4 σ -3.85 - 1×10 -12 σ + μ0

[0097]

[0098] From Figure 4 The specific expressions of the elastic modulus in the elastic region and the plastic region are fitted as follows:

[0099] E = - 2.1e (-σ / 17.22) + 0.12σ -2.7 + E0

[0100] E = - 2.1e (-σ / 17.22) + 0.12σ -2.7 - 2.5×10 4 γ p + E0

[0101] Step 9, in the seepage-invariant elastic region, the pore water pressure is fixed, resulting in a zero seepage force in this region. According to the boundary conditions in step 5), and based on the derivation formula of the classical Lame solution, the relationship between stress and displacement in the seepage-invariant elastic region can be obtained.

[0102]

[0103] The derivation formula of the classical Lame solution in the elastic region is as follows. Both A and C are constant coefficients and can be obtained from the boundary conditions.

[0104]

[0105] Step 10, the process of solving the stress-strain and displacement fields in the elastic zone includes:

[0106] a. The elastic strain of the i-th ring of rock mass provided by the generalized Hooke's law in step 4) and With the Biot effective stress σ′ r,(i) and σ′ θ,(i) Substitute the relational expressions between them into the deformation equations of the calculation formulas for the radial strain and tangential strain of the rock mass in step 3) of the present invention, and obtain Equation (1):

[0107]

[0108] Where the deformation equation is:[[]]END]]

[0109]

[0110] dr represents the derivative with respect to the radius r, represents the tangential elastic strain Derive with respect to the radius r;

[0111] b. Substitute the elastic strain and of the i-th ring of rock mass provided by the generalized Hooke's law in step 4) with the Biot effective stress σ′ r,(i) and σ′ θ,(i) Derive the tangential strain formula in the relational expressions between them, and further transform the derived formula by using the mechanical equilibrium equation of the rock mass in step 1), and obtain Equation (2):

[0112]

[0113] Where the derived formula is:[[]]END]]

[0114]

[0115] c. Combine the above Equation (1) and Equation (2), and an expression for the difference between the radial effective stress and the tangential effective stress of the rock mass can be obtained. Then, according to the boundary conditions in step 5) of the present invention, the seepage volume force formula, the mechanical equilibrium differential equation in step 1), and the expression of the pore water pressure in step 6), by performing ordinary differential integration on them, the radial effective stress of the i-th ring of rock mass can be obtained:[[]]END]]

[0116]

[0117] The seepage volume force in the above formula is

[0118] d. Substitute the radial effective stress in step 10)c into the mechanical equilibrium differential equation in step 1), and the tangential effective stress of the rock mass can be obtained:[[]]END]]

[0119]

[0120] e. Substitute the radial effective stress and the tangential effective stress in step 10)c and d into the elastic strain and in the relationship with the Biot effective stress σ r ′ ,(i) and σ′ θ,(i) and using the relationships among the radial strain, tangential strain and radial displacement in step 3), the radial displacement of the rock mass in the i-th ring in the elastic region can be obtained. The specific expression is as follows:

[0121]

[0122] f. According to the relationships among the radial strain, tangential strain and radial displacement in step 3), and combining with the radial displacement formula in step 10)e, the tangential strain of the rock mass can be obtained as:

[0123]

[0124] g. According to the stress and displacement formulas in the seepage-invariant elastic region in step 9), combining with the radial displacement formula in step 10)e and the boundary conditions at the adjacent rings where the pore water pressure changes, the recurrence equation of the radial effective stress of the rock mass in the elastic region can be obtained. Its expression is as follows:

[0125]

[0126] Where:

[0127]

[0128] The boundary condition of the outermost ring at the junction of the seepage-invariant elastic region and the seepage-varying elastic region is

[0129] Step 11. The process of solving the stress-strain and displacement fields in the plastic zone includes:

[0130] a. According to the yield criterion of the rock mass in the plastic state in step 2) of the present invention, the judgment criterion for the rock mass of the surrounding rock of the submarine tunnel to satisfy the Mohr-Coulomb yield criterion can be expressed as:

[0131]

[0132] b. Combining the seepage control equation in step 1) and the judgment criterion in step 11)a to obtain the expression of the first-order differential equation of the radial effective stress:

[0133]

[0134] c. Integrating the first-order differential equation of the radial effective stress in step 11)b and cooperating with the second boundary condition in step 5), the radial effective stress of the rock mass in the i-th ring can be obtained. The specific expression is as follows:

[0135]

[0136] Where: N i and Y i are two strength parameters of soft rock;

[0137]

[0138] d. Substitute the radial effective stress into the judgment criterion in step 11)a, and the tangential effective stress of the rock mass in the i-th ring can be obtained. The specific expression is:

[0139]

[0140] e. The relational expressions among the radial strain, tangential strain and radial displacement of the rock mass in the i-th ring in step 3), the relational expressions between elastic strain and plastic strain, and the elastic strain and and the Biot effective stress σ′ r,(i) and σ′ θ,(i) Substitute the relational expressions between them into the relational expression between the radial plastic strain and the tangential plastic strain in step 3) to obtain the differential equation of the radial displacement of the rock mass in the i-th ring:

[0141]

[0142] Then integrate the differential equation within the range of [R i , R i+1 , where R is the plastic radius and the subscript i represents the i-th ring; and using the second displacement boundary condition in step 5), the radial displacement of the rock mass in the i-th ring can be obtained:

[0143]

[0144] Where: κ i is the dilatancy coefficient,

[0145]

[0146]

[0147] f. According to the relational expressions among the radial strain, tangential strain and radial displacement in step 3), combined with the radial displacement formula in step 11)e, the tangential strain of the rock mass in the plastic zone can be obtained:

[0148]

[0149] Step 12. According to the plastic shear strain formula in step 3) and the relational expressions between elastic strain and plastic strain, the plastic shear strain of the surrounding rock of the submarine tunnel can be obtained. The specific expression is:

[0150]

[0151] Step 13: According to the radial displacement differential equation in step 11)e and combining with the plastic shear strain formula of the surrounding rock of the submarine tunnel in step 12), the calculation formula for the plastic shear strain in the plastic region of the surrounding rock of the submarine tunnel can be derived as follows:

[0152]

[0153] The embodiments described above are only descriptions of the preferred modes of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations, variations, modifications, and substitutions made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for calculating stress, strain and displacement fields of submarine tunnels under water-mechanical coupling conditions, characterized in that: The steps include: Step 1, the permeability of the surrounding rock mass of the submarine tunnel is expressed by the seepage volume force, and the seepage volume force and the mechanical equilibrium differential equation of the i-th ring rock mass are used as the seepage control equation; Step 2, using the linear Mohr-Coulomb yield criterion as the governing equation of the plastic state; Step 3, using plastic shear strain as a softening parameter, and taking the plastic shear strain, the relationship between the radial strain, tangential strain and radial displacement of the i-th ring rock mass, the relationship between the elastic strain and the plastic strain, and the relationship between the radial plastic strain and the tangential plastic strain as the control equation of the rock mass strain softening phenomenon; Step 4: Provide the elastic strain of the rock mass in the i-th ring by generalized Hooke's law and and Biot effective stress σ r ' ,(i) and σ′ θ,(i) The relationship between and is used to obtain the seepage differential equation of the i-th ring rock mass; in, and are the radial elastic strain and tangential elastic strain of the tunnel surrounding rock, σ r ' ,(i) and σ′ θ,(i) are radial effective stress and tangential effective stress respectively; Step 5, by setting boundary conditions, ensure that the radial effective stress, pore water pressure and displacement of the surrounding rock of the submarine tunnel are continuous at the adjacent ring boundaries; Step 6, obtaining the pore water pressure of each ring of rock mass according to the seepage differential equation in step 4 and the boundary conditions in step 5; Step 7: The water inflow of each ring of rock mass is a constant value, that is: Q1=…=Q n =Q Where Q is the rock mass water inflow used in the calculation; The water inflow of the rock mass is obtained by calculation, and the expression of pore water pressure is updated at the same time; Step 8, the degree of destruction of rock mass fissures is expressed by plastic strain, and nonlinear surface fitting is performed on the sorted permeability coefficient test data to obtain nonlinear surface fitting formulas for permeability coefficient, Biot coefficient, Poisson's ratio and elastic modulus affected by confining pressure and plastic shear strain; Step 9, according to the boundary conditions in step 5, the stress and displacement in the seepage invariant elastic region are obtained; Step 10, solving the stress, strain and displacement fields in the elastic region; Step 11, solving the stress, strain and displacement fields in the plastic zone; The step 10 includes: a. Substitute the relationship between the elastic strain of the i-th ring rock mass and the Biot effective stress in step 4 into the deformation equation of the radial strain and tangential strain calculation formula of the rock mass in step 3 to obtain equation (1: Where r is the calculated radius of the i-th ring rock mass, G i is the shear modulus, dr represents the derivative with respect to the radius r, represents the tangential elastic strain Derivative with respect to radius r; b, the elastic strain of the i-th ring rock mass in step 4 and and Biot effective stress σ r ' ,(i) and σ′ θ,(i) The tangential strain formula in the relationship is derived, and the mechanical equilibrium equation of the rock mass in step 1 is used to further transform the derived formula to obtain equation (2: In the formula, μ i is Poisson’s ratio; c. Combining equation (1) and equation (2), the expression of the difference between the radial effective stress and the tangential effective stress of the rock mass is obtained; by performing ordinary differential integration on the boundary conditions in step 5, the seepage volume force formula and the mechanical equilibrium differential equation in step 1, and the expression of the pore water pressure in step 6, the radial effective stress of the rock mass in the i-th ring is obtained; d. Substitute the radial effective stress in c into the mechanical equilibrium differential equation in step 1 to obtain the tangential effective stress of the rock mass; e. Substitute the radial effective stress and tangential effective stress in c and d into the elastic strain of the rock mass in the i-th ring in step 4. and and Biot effective stress σ r ' ,(i) and σ′ θ,(i) In the relationship between, the radial displacement of the i-th ring rock mass in the elastic region is obtained by using the relationship between the radial strain, tangential strain and radial displacement in step 3; f. According to the relationship between radial strain, tangential strain and radial displacement in step 3, combined with the radial displacement formula in e, the tangential strain of the rock mass is obtained; g. According to the stress and displacement formulas in the elastic region with constant seepage in step 9, combined with the radial displacement formula in e and the boundary conditions at the adjacent rings where the pore water pressure changes, the recursive equation for the radial effective stress of the rock mass in the elastic region is obtained.

2. The calculation method according to claim 1, characterized in that: The step 11 includes: a. The judgment criteria for whether the surrounding rock mass of a submarine tunnel meets the Mohr-Coulomb yield criterion are expressed as follows: In the formula, c i and are the cohesion and internal friction angle of the rock mass respectively; b. Combine the seepage control equation in step 1 and the judgment criteria in step a to obtain the first-order differential equation expression of radial effective stress; c. Integrate the first-order differential equation of radial effective stress in b, and combine it with the boundary conditions in step 5 to obtain the radial effective stress of the i-th ring rock mass; d. Substitute the radial effective stress into the judgment criterion in a to obtain the tangential effective stress of the i-th ring rock mass; e. The relationship between the radial strain, tangential strain and radial displacement of the i-th ring rock mass in step 3 and the relationship between the elastic strain and plastic strain and the elastic strain in step 4 and and Biot effective stress σ r ' ,(i) and σ′ θ,(i) Substitute the relationship between the radial plastic strain and the tangential plastic strain in step 3 to obtain the radial displacement differential equation of the i-th ring rock mass. Then, the differential equation is replaced by [R i ,R i+1 ] and use the boundary conditions in step 5 to obtain the radial displacement of the rock mass in the i-th ring; Where R is the plastic radius, and the subscript i represents the i-th ring; f. According to the relationship between radial strain, tangential strain and radial displacement in step 3, combined with the radial displacement formula in e, the tangential strain of the rock mass in the plastic zone is obtained.

3. The calculation method according to claim 2, characterized in that: Also includes: Step 12, according to the plastic shear strain formula in step 3 and the relationship between elastic strain and plastic strain, obtain the plastic shear strain of the surrounding rock of the submarine tunnel; Step 13, based on the radial displacement differential equation in step e of step 11 and the plastic shear strain formula of the surrounding rock of the submarine tunnel in step 12, derive the calculation formula of the plastic shear strain in the plastic zone of the surrounding rock of the submarine tunnel.

4. The calculation method according to claim 1, characterized in that: The seepage volume force in step 1 is expressed as: The mechanical equilibrium differential equation of the i-th ring rock mass in step 1 is expressed as: in: is the pore water pressure of the i-th ring rock mass, r is the calculated radius of the i-th ring rock mass; S i is the seepage volume force; subscript i is r=R i The variable value corresponding to the rock mass of the ith ring at time; β is the Biot coefficient, K is the bulk modulus of soil, K s is the bulk modulus of soil particles; dr represents the derivative with respect to radius r, represents the radial effective stress σ r ' ,(i) Derivative with respect to radius r; The linear Mohr-Coulomb yield criterion in step 2 is expressed as: Where H is the function of the radial effective stress and plastic shear strain of the surrounding rock; H is represented by: In the formula, c i and are the cohesion and internal friction angle of the rock mass respectively; The plastic shear strain in step 3 is expressed as: Where: is the plastic shear strain of the i-th ring rock mass; The relationship between the radial strain, tangential strain and radial displacement of the i-th ring rock mass in step 3 is expressed as: Where: ε r,(i) and ε θ,(i) is the radial strain and tangential strain of the tunnel surrounding rock; u (i) is the radial displacement of the surrounding rock, r is the calculated radius of the i-th ring rock mass; The relationship between elastic strain and plastic strain in step 3 is expressed as: The relationship between the radial plastic strain and the tangential plastic strain in step 3 is expressed as: In the formula, ψ i is the dilatancy angle of the ith ring rock mass.

5. The calculation method according to claim 1, characterized in that: The relationship between the elastic strain of the i-th ring rock mass and the Biot effective stress in step 4 is expressed as: Where: G i is the shear modulus; μ i is Poisson's ratio; p0′ is the hydrostatic ground effective stress; The specific expression of the seepage differential equation of the i-th ring rock mass in step 4 is: Where: is the pore water pressure of the i-th ring rock mass; The specific expression of the boundary condition of the water-mechanical coupling analytical solution in step 5 is: Where: For r≥R u Initial pore water pressure at ; is the pore water pressure when r=R1; σ r ' ,1 is the radial effective stress when r=R1; σ r ' (n) is the radial effective stress when the radius tends to infinity; The specific expression of pore water pressure in step 6 is: Where: γ w is the density of water; Q i is the water inflow of the i-th ring rock mass; k i is the permeability coefficient of the i-th ring rock mass; The specific expression of water inflow in step 7 is: In the formula, R is the plastic radius, j represents the jth ring, j = i + 1; The updated pore water pressure expression in step 7 is:

6. The calculation method according to claim 1, characterized in that: The specific expressions of stress and displacement in the seepage invariant elastic region in step 9 are:

7. The calculation method according to claim 1, characterized in that: The deformation equation in a in step 10 is: The formula after derivation in step 10 b is: The specific expression of the radial effective stress of the i-th ring rock mass in c in step 10 is: The permeability volume force in the above formula is The specific expression of the tangential effective stress of the rock mass in the i-th ring in step 10 is: The specific expression of the radial displacement in e in step 10 is: in, The specific expression of the tangential strain in f in step 10 is: The specific expression of the radial effective stress recursion equation in step 10 is: in: The boundary condition of the outermost ring at the junction of the invariant elastic region and the variable elastic region is 8. The calculation method according to claim 2, characterized in that: The specific expression of the first-order differential equation of radial effective stress in step 11b is: The specific expression of the radial effective stress in c in step 11 is: Where: N i and Y i are two strength parameters of soft rock; The specific expression of the tangential effective stress in d in step 11 is: The specific expression of the radial displacement differential equation in step 11 is: The specific expression of radial displacement in e in step 11 is: Where: i is the shear dilatancy coefficient, The specific expression of the rock mass tangential strain in f in step 11 is:

9. The calculation method according to claim 3, characterized in that: The specific expression of the plastic shear strain of the surrounding rock of the submarine tunnel in step 12 is: The specific expression of the calculation formula of the plastic shear strain in the plastic zone of the surrounding rock of the submarine tunnel in step 13 is:

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